Excess noise in a topological SNS junction between chiral Majorana liquids

Abstract: We consider a Josephson contact mediated by 1D chiral modes on a surface of a 3D topological insulator with superimposed superconducting and magnetic layers. The system represents an interferometer in which 1D chiral Majorana modes on the boundaries of superconducting electrodes are linked by ballistic chiral Dirac channels. This model may be realized also in recently fabricated heterostructures based on quantum anomalous Hall insulators (QAHI). Our system is a single-channel ballistic Josephson junction where the Andreev pairs can be thought of as being the scattering states of the incident Majorana fermions in the leads. We investigate the noise of the Josephson current as a function of the dc phase bias and the Aharonov-Bohm flux. Starting from the scattering formalism, a Majorana representation of the Keldysh generating action for the full counting statistics of the transmitted charge is found. The generalized Levitov-Lesovik formula, defined in terms of quantum counting field, was derived. It allows one to calculate cumulants of transmitted charge between the superconductors. In particular, an expression for the zero-frequency noise follows from the second-order expansion in the counting field. We find that quantum transport reveals rich behavior at temperatures lower than the Thouless energy. It is manifested in oscillations of the noise power as a function of the superconducting and the Aharonov-Bohm phases, in current-phase relation singularities and in the fractional h/e-periodicity of a critical current [1,2], and in the emerging of large dissipative part of the impedance in addition to the usual Josephson inductive part [3].

References
[1] D.S. Shapiro, A. Shnirman, and A.D. Mirlin, Phys. Rev. B, 93, 155411 (2016).
[2] D.S. Shapiro, D.E. Feldman, A.D. Mirlin, and A. Shnirman, Phys. Rev. B, 95, 195425 (2017).
[3] D.S. Shapiro, A.D. Mirlin, A. Shnirman, Phys. Rev. B, 98, 245405 (2018).